Practice Linear Programming (11.2.1) - Reductions - Design & Analysis of Algorithms

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9 questions

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6 sample questions

Question 1.
What is the purpose of linear programming?
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Think about optimization in terms of resources.
Question 2.
Define a bipartite graph in simple terms.
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Consider how people and jobs might be matched.
3Question 3.
What is linear programming primarily used for?
- Maximizing profits
- Finding shortest paths
- Simulating network traffic
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Think about business applications.
4Question 4.
True or False: A bipartite graph can have edges connecting vertices within the same set.
- True
- False
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Visualize the structure of bipartite graphs.
Question 5.
Given 5 teachers and 4 courses, design a flow network to illustrate maximum matching. Consider some teachers have preferences for more than one course.
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Think about how to ensure the flow meets the allocation constraints.
Question 6.
If a new constraint is added where teachers can teach a maximum of two courses, re-evaluate the original matching model and discuss the implications on the network flow.
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Consider how this relaxation of constraints alters the network structure.

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